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The regulation of galaxy growth along the size-mass relation by star-formation, as traced by H$α$ in KMOS$^{3D}$ galaxies at 0.7 < z < 2.7

We present half-light sizes measured from H$α$ emission tracing star-formation in 281 star-forming galaxies from the KMOS3D survey at 0.7 < z < 2.7. Sizes are derived by fitting 2D exponential disk models, with bootstrap errors averaging 20%. H$α$ sizes are a median (mean) of 1.19 (1.26) times larger than those of the stellar continuum, which due to radial dust gradients places an upper limit on the growth in stellar size via star formation, with just 43% intrinsic scatter. At fixed continuum size the H$α$ size shows no residual trend with stellar mass, star formation rate, redshift or morphology. The only significant residual trend is with the excess obscuration of H$α$ by dust, at fixed continuum obscuration. The scatter in continuum size at fixed stellar mass is likely driven by the scatter in halo spin parameters. The stability of the ratio of H$α$ size to continuum size demonstrates a high degree of stability in halo spin and in the transfer of angular momentum to the disk over a wide range of physical conditions and cosmic time. This may require local regulation by feedback processes. The implication of our results, as we demonstrate using a toy model, is that our upper limit on star-formation driven growth is sufficient only to evolve star-forming galaxies approximately along the observed size-mass relation, consistent with the size growth of galaxies at constant cumulative co-moving number density. To explain the observed evolution of the size-mass relation of star-forming disk galaxies other processes, such as the preferential quenching of compact galaxies or galaxy mergers, may be required.